Eamon Sheridan's first league goal for Finn Harps was not enough to keep the cup finalists in the race for third place. Instead, his strike was wiped out by an 85th-minute penalty from Sligo's Marcus Hallows.
Sheridan, in for the injured Jonathan Speak, had hit the bar in the 23rd minute, but he made no mistake in the 41st minute when he lobbed Mat Boswell from the edge of the box.
Harps had lost their previous two games, and their hopes of taking all three points were made more difficult in the 62nd minute when Trevor Scanlon was sent off for a second bookable offence.
Sligo were handed a lifeline when Shane Bradley's clearance hit Minnock on the hand and Marcus Hallows made no mistake with the penalty kick.
Finn Harps: McKenna; Scanlon, Minnock, Bradley, Dykes, Kavanagh, Mohan, McGettigan, Sheridan, Mulligan, Harkin. Subs: McHugh for Sheridan (58 mins), Nash for Harkin (65 mins), R Boyle for Mulligan (80 mins).
Sligo Rovers: Boswell, McLynn, Hutchinson, O'Grady, Charles, Sheridan, Kennedy, Birks, Hallows, Hoeks, Lynch. Sub: Shannon for Kennedy (half-time). Referee: P Whelan (Dublin).